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Question 4
A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre. The data for annual rainfall was coded using $v = \frac{x - 5... show full transcript
Step 1
Answer
To find the regression line, we first need to determine the slope (b) and the y-intercept (a).
The slope b is calculated using the formula:
Substituting the values:
Next, we calculate the intercept a using:
Substituting in the known values:
Thus, the equation of the regression line is:
Step 2
Answer
To estimate the yield when cm, we first compute the coded value v:
Next, substitute v into the regression equation:
Calculating this gives:
Therefore, the estimated annual yield of peas per acre when the annual rainfall is 85 cm is approximately 3.95 tonnes.
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